Properties

Label 6001.2.a.c
Level 6001
Weight 2
Character orbit 6001.a
Self dual Yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(0\)
Dimension: \(121\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(121q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 127q^{4} \) \(\mathstrut +\mathstrut 21q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut -\mathstrut 13q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 134q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(121q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 127q^{4} \) \(\mathstrut +\mathstrut 21q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut -\mathstrut 13q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 134q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut +\mathstrut 40q^{11} \) \(\mathstrut +\mathstrut 41q^{12} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 32q^{14} \) \(\mathstrut +\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 135q^{16} \) \(\mathstrut -\mathstrut 121q^{17} \) \(\mathstrut +\mathstrut 28q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 34q^{21} \) \(\mathstrut -\mathstrut 18q^{22} \) \(\mathstrut +\mathstrut 37q^{23} \) \(\mathstrut +\mathstrut 54q^{24} \) \(\mathstrut +\mathstrut 128q^{25} \) \(\mathstrut +\mathstrut 91q^{26} \) \(\mathstrut +\mathstrut 55q^{27} \) \(\mathstrut -\mathstrut 28q^{28} \) \(\mathstrut +\mathstrut 45q^{29} \) \(\mathstrut +\mathstrut 30q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 40q^{33} \) \(\mathstrut -\mathstrut 9q^{34} \) \(\mathstrut +\mathstrut 59q^{35} \) \(\mathstrut +\mathstrut 138q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut +\mathstrut 37q^{39} \) \(\mathstrut +\mathstrut 14q^{40} \) \(\mathstrut +\mathstrut 89q^{41} \) \(\mathstrut +\mathstrut 33q^{42} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 90q^{44} \) \(\mathstrut +\mathstrut 83q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 135q^{47} \) \(\mathstrut +\mathstrut 96q^{48} \) \(\mathstrut +\mathstrut 128q^{49} \) \(\mathstrut +\mathstrut 71q^{50} \) \(\mathstrut -\mathstrut 13q^{51} \) \(\mathstrut +\mathstrut 47q^{52} \) \(\mathstrut +\mathstrut 52q^{53} \) \(\mathstrut +\mathstrut 90q^{54} \) \(\mathstrut +\mathstrut 93q^{55} \) \(\mathstrut +\mathstrut 69q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 170q^{59} \) \(\mathstrut +\mathstrut 78q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 182q^{64} \) \(\mathstrut +\mathstrut 50q^{65} \) \(\mathstrut +\mathstrut 68q^{66} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut -\mathstrut 127q^{68} \) \(\mathstrut +\mathstrut 97q^{69} \) \(\mathstrut +\mathstrut 46q^{70} \) \(\mathstrut +\mathstrut 191q^{71} \) \(\mathstrut +\mathstrut 57q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 68q^{74} \) \(\mathstrut +\mathstrut 86q^{75} \) \(\mathstrut +\mathstrut 108q^{76} \) \(\mathstrut +\mathstrut 62q^{77} \) \(\mathstrut -\mathstrut 10q^{78} \) \(\mathstrut +\mathstrut 130q^{80} \) \(\mathstrut +\mathstrut 149q^{81} \) \(\mathstrut +\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 83q^{83} \) \(\mathstrut +\mathstrut 126q^{84} \) \(\mathstrut -\mathstrut 21q^{85} \) \(\mathstrut +\mathstrut 132q^{86} \) \(\mathstrut +\mathstrut 50q^{87} \) \(\mathstrut -\mathstrut 42q^{88} \) \(\mathstrut +\mathstrut 144q^{89} \) \(\mathstrut +\mathstrut 9q^{90} \) \(\mathstrut +\mathstrut 13q^{91} \) \(\mathstrut +\mathstrut 50q^{92} \) \(\mathstrut +\mathstrut 43q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut +\mathstrut 82q^{95} \) \(\mathstrut +\mathstrut 110q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 89q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.80099 1.23587 5.84553 −1.08657 −3.46165 −3.96716 −10.7713 −1.47263 3.04347
1.2 −2.75847 −2.11283 5.60915 3.70679 5.82818 −2.88565 −9.95572 1.46406 −10.2251
1.3 −2.69106 2.90048 5.24179 1.92081 −7.80536 −1.20204 −8.72383 5.41280 −5.16901
1.4 −2.63511 −2.54509 4.94380 −1.75130 6.70660 −0.500367 −7.75725 3.47750 4.61488
1.5 −2.61678 −3.27387 4.84754 0.197154 8.56700 −1.64878 −7.45139 7.71823 −0.515910
1.6 −2.60140 −0.594038 4.76726 2.91382 1.54533 0.0965456 −7.19873 −2.64712 −7.57999
1.7 −2.58940 0.995654 4.70501 0.868437 −2.57815 −0.888525 −7.00437 −2.00867 −2.24873
1.8 −2.54984 3.38084 4.50169 −1.07763 −8.62059 1.13594 −6.37892 8.43005 2.74778
1.9 −2.53200 0.341990 4.41103 2.95840 −0.865919 4.74675 −6.10474 −2.88304 −7.49068
1.10 −2.48167 1.61831 4.15867 −3.04222 −4.01610 0.428830 −5.35710 −0.381079 7.54977
1.11 −2.44940 0.192595 3.99956 1.46027 −0.471742 −3.96634 −4.89773 −2.96291 −3.57679
1.12 −2.29935 −2.65633 3.28702 −0.0208883 6.10783 4.05842 −2.95931 4.05607 0.0480296
1.13 −2.25146 1.98627 3.06909 4.11708 −4.47201 2.76168 −2.40701 0.945268 −9.26946
1.14 −2.24876 −0.983386 3.05693 −2.62112 2.21140 0.682123 −2.37679 −2.03295 5.89428
1.15 −2.22966 1.54651 2.97139 −1.67307 −3.44820 −3.79558 −2.16587 −0.608295 3.73037
1.16 −2.18200 −1.07317 2.76112 −3.39433 2.34166 −4.74202 −1.66076 −1.84830 7.40643
1.17 −2.13704 −0.352862 2.56694 0.777890 0.754080 0.156355 −1.21157 −2.87549 −1.66238
1.18 −2.08608 1.06648 2.35172 −3.22907 −2.22475 0.560788 −0.733710 −1.86263 6.73610
1.19 −2.05839 1.11600 2.23697 1.51993 −2.29716 0.698036 −0.487784 −1.75454 −3.12862
1.20 −2.05373 −1.71490 2.21782 −3.91336 3.52195 1.58894 −0.447336 −0.0591109 8.03700
See next 80 embeddings (of 121 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.121
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(17\) \(1\)
\(353\) \(-1\)